Geodesic
Asymptotics of the solution of the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a slender cylinder
Izvestiya. Mathematics, Tome 18 (1982) no. 1, pp. 145-161 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Dirichlet problem is investigated for the Laplace and Helmholtz equations in the exterior of a surface in $\mathbf R^3$ which is a right circular cylinder outside a sphere. Asymptotic expansions of the solutions are constructed; the small parameter is the maximal diameter of the cross-section of the cylinder. Bibliography: 8 titles. 
@article{IM2_1982_18_1_a7,
     author = {M. V. Fedoryuk},
     title = {Asymptotics of the solution of the {Dirichlet} problem for the {Laplace} and {Helmholtz} equations in the exterior of a~slender cylinder},
     journal = {Izvestiya. Mathematics},
     pages = {145--161},
     year = {1982},
     volume = {18},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1982_18_1_a7/}
}
TY  - JOUR
AU  - M. V. Fedoryuk
TI  - Asymptotics of the solution of the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a slender cylinder
JO  - Izvestiya. Mathematics
PY  - 1982
SP  - 145
EP  - 161
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1982_18_1_a7/
LA  - en
ID  - IM2_1982_18_1_a7
ER  - 
%0 Journal Article
%A M. V. Fedoryuk
%T Asymptotics of the solution of the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a slender cylinder
%J Izvestiya. Mathematics
%D 1982
%P 145-161
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1982_18_1_a7/
%G en
%F IM2_1982_18_1_a7
M. V. Fedoryuk. Asymptotics of the solution of the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a slender cylinder. Izvestiya. Mathematics, Tome 18 (1982) no. 1, pp. 145-161. http://geodesic.mathdoc.fr/item/IM2_1982_18_1_a7/

[1] Mischenko E. F., Pontryagin L. S., “Ob odnoi statisticheskoi zadache optimalnogo upravleniya”, Izvestiya AN SSSR. Seriya matem., 25 (1961), 477–498 | Zbl

[2] Ilin A. M., “Kraevaya zadacha dlya ellipticheskogo uravneniya vtorogo poryadka v oblasti s uzkoi schelyu. I: Dvumernyi sluchai”, Matem. sb., 99:4 (1976), 514–537 | MR

[3] Ilin A. M., “Kraevaya zadacha dlya ellipticheskogo uravneniya vtorogo poryadka v oblasti s uzkoi schelyu. II: Oblast s malym otverstiem”, Matem. sb., 103:2 (1977), 265–284 | MR

[4] Van Daik, Metody vozmuschenii v mekhanike zhidkosti, Mir, M., 1967 | Zbl

[5] Koul Dzh., Metody vozmuschenii v prikladnoi matematike, Mir, M., 1972 | MR

[6] Khenl X., Maue A., Vestfall K., Teoriya difraktsii, Mir, M., 1964

[7] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1966 | MR | Zbl

[8] Malyuzhinets G. D., “Matematicheskaya formulirovka zadachi o vynuzhdennykh garmonicheskikh kolebaniyakh v proizvolnoi oblasti”, Dokl. AN SSSR, 78:3 (1951), 78–80